Non-parametric estimation of bivariate reliability from incomplete two-dimensional warranty data

A two-dimensional warranty coverage is available for those items for which age and usage jointly fall below the respective warranty limits, thus making the warranty field data incomplete. In this paper, the joint reliability function of age and usage from the observed incomplete two-dimensional warranty data has been estimated in terms of reliability function and density function of age and usage rate respectively by using non-parametric method under the assumption of independence between age and usage rate. Bivariate mean residual life for age and usage has also been determined using the bivariate reliability function. From the reliability engineering perspective, mean residual life provides valuable information for various decision making problems, such as optimizing burn-in test, extending warranty policy, and making maintenance decision. In this paper, the mean residual life has been predicted for formulating extended warranty policy. Pro-rata warranty policy has also been considered here using linear and non-linear pro-rata functions. The utilities of this research work have been demonstrated with the help of a real-life warranty data set.